The first operation should be to get one of your coefficients to be equal to the negative of one from the other equation(same variable).
so you have a 5x and a 6x. to go from 5->6 you multiply by 6/5. Its always a ratio of the two, where the number your going to is in the numerator and the number your coming from is in the denominator.
Now you multiply the whole equation containing 5x by that fraction
Now the coefficients match between the two equation but we want the negative so when we add the equations they will cancel. So we just multiply everything by (-1) or flip the sign
And add them together
combine the fractions over a common denominator
Isolate the y by multiplying the inverse of its coefficient
Now that you have y just plug it back into any equation with both y and x.
The solution you get is the intersection of the two equations. These equations have two variables which makes them lines. If you graph both these lines they will intersect at (2,10) or (x=2,y=10) as seen in the graph below